分数占据原子的全数值计算。值域分离交换泛函
Fully numerical calculations on atoms with fractional occupations. Range-separated exchange functionals
摘要：
最近发展的一种全数值原子结构计算的有限元方法[S. Lehtola，Int. J. Quantum Chem. 119，e25945（2019）]扩展到通过分数占据轨道描述具有球对称密度的原子。专门版本的Hartree-Fock以及局域密度和广义梯度近似密度泛函的开发，允许非常快速的计算在基组限制的地面和低洼的激发态，甚至重原子。还描述了基于Yukawa或互补误差函数（erfc）内核的范围分离的实现，允许现代范围分离混合泛函的整数或分数占用数的完整基组基准。最后，在局域密度或广义梯度近似水平上，计算了原子有效势的叠加原子势方法[S。Lehtola，J. Chem. Theory Comput. 15，1593（2019）]，其已被证明是初始化电子结构计算的简单且有效的方式。本数值方法提供超越microhartree精度与少量的数值基函数，并重现文献结果的基态原子和它们的阳离子$1 \leq Z \leq 86 $。我们的研究结果表明，文献值偏离了10 μEh从完整的基组极限。数值方案的erfc内核的工作比较从大高斯基组计算的结果从文献中。自旋限制基态的报告Hartree-Fock和Hartree-Fock-Slater计算与分数占用$1 \leq Z \leq 118$。
英文摘要：
A recently developed finite element approach for fully numerical atomic structure calculations [S. Lehtola, Int. J. Quantum Chem. 119, e25945 (2019)] is extended to the description of atoms with spherically symmetric densities via fractionally occupied orbitals. Specialized versions of Hartree-Fock as well as local density and generalized gradient approximation density functionals are developed, allowing extremely rapid calculations at the basis set limit on the ground and low-lying excited states even for heavy atoms. The implementation of range-separation based on the Yukawa or complementary error function (erfc) kernels is also described, allowing complete basis set benchmarks of modern range-separated hybrid functionals with either integer or fractional occupation numbers. Finally, computation of atomic effective potentials at the local density or generalized gradient approximation levels for the superposition of atomic potentials (SAP) approach [S. Lehtola, J. Chem. Theory Comput. 15, 1593 (2019)] that has been shown to be a simple and efficient way to initialize electronic structure calculations is described. The present numerical approach is shown to afford beyond microhartree accuracy with a small number of numerical basis functions, and to reproduce literature results for the ground states of atoms and their cations for $1 \leq Z \leq 86 $. Our results indicate that the literature values deviate by up to 10 μEh from the complete basis set limit. The numerical scheme for the erfc kernel is shown to work by comparison to results from large Gaussian basis set calculations from the literature. Spin-restricted ground states are reported for Hartree-Fock and Hartree-Fock-Slater calculations with fractional occupations for $1 \leq Z \leq 118$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
